One way to compare
the branches is to add together the two output measures to
obtain a single measure. The table below shows the combined
outputs with the title *transactions*. The number of
transactions is simply the sum of the personal
and business transactions shown in the data table.
With only one output and one input we can compare DMU's by
computing the ratio: output/input or transactions per staff
member. The *Ratio *column
is obtained by dividing the transactions
number by the staff number. This suggests that Croydon is
the best branch because its ratio is larger than all the rest.
For convenience we want a measure
that lies between 0 and 1, so we divide the ratios by the maximum
ratio (9.72). The results for the four branches are in the
column above labeled *Efficiency*.
Efficiency is a good word for the measure since it divides output
by input and is similar to comparisons made in other fields.
For instance one can speak of the efficiency of a solar
cell by dividing the electrical power produced in the cell
by the light power falling on the cell. Both
input and output power are measured in watts.
The quantities are difficult to measure, but efficiency compares
the result to a standard to obtain a meaningful value. For
instance the record for solar cell efficiency is 42%.
One would expect that solar cell efficiency will never approach
1.
The efficiency
number computed in the table above is not the same. The
value of 1 does not mean Croydon is perfectly translating inputs to outputs.
It only means that Croydon has the best output over input ratio of the four
banks. If one accepts the measure it can be used to rank the four DMU's. The
result is shown in the rank column. The CFO
has the result that she needs. She brings her ranking to a meeting with the
branch managers.
The manager of the Croydon branch is pleased, but the other
branch managers call the ranking unfair. They say the measure
used to obtain the ranking is flawed. Simply adding the outputs
may not be correct. Different efficiencies would be obtained
if a different weight were applied to each measure. One could
say that the personal transactions were not as important as
the business transactions. Someone could propose that each business
transition be given three times the weight of a personal transaction.
This would yield different efficiency values and perhaps a different
ranking.
The CFO does not want to pursue a policy that alienates
the managers. No one, except the Croydon
bank manager will accept the efficiency as calculated above to compute the
ranking. If the branch managers accept the idea that some ratio of outputs
to inputs can be used for comparison, the problem is to agree on
the best weights for the output factors. Of course, the branch managers
will not agree on the appropriate weights.
The operations analyst attending the meeting suggests to the CFO that the
DEA method might help in seeking agreement. After a private discussion with
the analyst, the CFO announces that the managers may independently weigh the
factors
any way they like. The CFO adds that the managers must each use
the input and output data (from the tables above) and
evaluate the efficiencies for all four branches with the same set of weights.
Each branch must work without interacting with any other branch. The managers
agree to the restrictions and agree to meet in one week to provide
their answers.
DEA is a method to deal with situations like this. Although it does not solve
the ranking problem directly, the DEA provides some objective measures to obtain
a partial ranking. The DEA add-in embodies the computational tools necessary
to implement the method.The following pages of this section describe the method
along with the add-in features. Only the basics of DEA are presented. There
are many papers and books on the subject as reported in a web site by Emrouznejad.
Several commercial programs provide more detailed analysis than this add-in.
There are many practical questions involved with actual implementations that
are not considered here. |